Assignment 2(Math 1131A)

: Is there a correlation between test anxiety and exam score performance? Data on x = score on a measure of test and y = exam score for a sample of n=9 students are the following (the data are consistent with summary quantities given in the paper “ Effects of Humor on Test Anxiety and Performance,” Psychological Reports [1999]: 1203-1212):

x: 23 14 14 0 17 20 20 15 21

y: 43 59 48 77 50 52 46 51 51

Higher values for x indicate higher levels of anxiety.

  1. Construct a scatterplot, and comment on the features of the plot.
  2. Does there appear to be a linear relationship between the two variables? Based on the scatterplot, would you characterize the relationship as positive or negative? Strong or weak?
  3. Compute the value of the correlationcoefficient. Is the valur of r consistent with your answer to Part (b)?
  4. Based on the value of thecorrelation, is it reasonable to conclude that test anxiety caused poor exam performance? Explain.

: According to the article “ First-Year Academic Success: A Prediction Combining Cognitive and Psychosocial Variables for Caucasian and African American Students”(Journal of College Student Development[1999]:599-605), high school GPA(x) and first year college GPA(y) are mildly correlated. The data, which were collected from a Southeastern public research university, can be summarized as follows:

n=2600,

  1. Find the equation of the least squares regression line.
  2. Interpret the value of b, the slope of the least squares line, in the context of this problem.
  3. C. What first-year GPA would you predict for a student with a 4.0 high schhol GPA?

: Refer to the following information on births in the United States over a given perion of time:

Type of Birth Number of Births

Single birth 41,500,000

Twins 500,000

Triplets 5000

Quadruplets 100

Use this information to approximate the probability that a randomly selected pregnant woman who reaches full term

  1. Delivers twins
  2. Delivers quadruplets
  3. Gives birth to more than a single child.

Problem 6.20(Page 293): A mutual fund company offers its customers several different funds; a money market fund, three different bond funds (short-, intermediate-, and long- term0 two stock funds ( moderate- and high risk), and a balanced fund. Among customers who own shares in just one fund, the percentages of customers in the different funds are as follows:

Money market 20%

Short-term bond 15%

Intermediate-term bond 10%

Long-term bond 5%

High-risk stock 18%

Moderate-risk stock 25%

Balanced fund 7%

A customer who owns shares in just one fund is randomly selected

a. What is the probability that the selected individual owns shares in the balanced fund?

b. What is the probability that the individual owns shares in a bond fund.

c. What is the probability that the individual does not own shares in a stock fund?

Problem 6.36 (Page 304): A Gallup Poll conducted in November 2002 examined how people perceive the risks associated with smoking. The following table summarizes data on smoking status and perceived risk of smoking and is consistent with summary quantities published by Gallup:

Perceived Risk
Smoking Status / Very
Harmful / Somewhat
Harmful / Not Too Harmful / Not At All Harmful
Current Smoker / 60 / 30 / 5 / 1
Former Smoker / 78 / 16 / 3 / 2
Never Smoked / 86 / 10 / 2 / 1

Assume that it is reasonable to consider these data as representative of the U.S. adult population.

  1. What is the probability that a randomly selected U.S. adult is a former smoker?
  2. What is the probability that a randomly selected U.S. adult views smoking as very harmful?
  3. What is the probability that a randomly selected U.S. adult views smoking as very harmful given that the selected individual is a current smoker?
  4. What is the probability that a randomly selected U.S. adult views smoking as very harmful given that the selected individual is a former smoker?
  5. What is the probability that a randomly selected U.S. adult views smoking as very harmful given that the selected individual never smoked?
  6. How do the probabilities computed in Parts (c), (d) and (e) compare? Does this surprise you? Explain.

Problem 6.48(Page313): Approximately 30% of the calls to an airline reservation phone line result in a reservation being made.

  1. Suppose that an operator handles 10 calls. What is the probability that none of the 10 calls result in a reservation?
  2. What assumption did you make to calculate the probability in Part (a)?
  3. What is the probability that at least one call results in a reservation being made?

Problem 6.60((Page 325): A construction firm bids on two different contracts. Let E1 be the event that the bid on the first contract is successful, and define E2 analogously for the second contract. Suppose that P(E1) = .4 and P(E2) = .3 and thatE1 and E2 are independent events.

  1. Calculate the probability that both bids are successful(the probability of the event E1 and E2)
  2. Calculate the probability that neither bid is successful( the probability of the event (not E1) and (not E2)).
  3. What is the probability that the firm is successful in at least one of the two bids?